Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 950 · 40 questions

How to solve it (Name the topic, then solve): Name the topic first: angles, counting, worst case, probability, digits, mensuration, data, coordinates, AP, algebra, primes or Venn diagrams. Use that lesson’s method; draw a quick sketch, list or Venn diagram on rough paper. Rule out options of the wrong kind — a probability above 1, or a triangle angle of 180° or more. Check by working backwards or with a second method when you can.

1. 1.What is the median of 36, 11, 15, 21, 9, 26 and 31? (a) 26 (b) 15 (c) 22 (d) 21
2. 2.In a class of 35 children, 22 like mangoes, 7 like bananas and 2 like both. How many like neither? (a) 8 (b) 6 (c) 2 (d) 10
3. 3.In a class of 36 children, 20 like cricket, 19 like football and 2 like neither. How many like both? (a) 34 (b) 3 (c) 5 (d) 2
4. 4.A canteen sells 5 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 40 (b) 12 (c) 35 (d) 70
5. 5.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 24 (b) 25 (c) 13 (d) 12
6. 6.How many prime numbers are there between 10 and 20? (a) 6 (b) 5 (c) 4 (d) 3
7. 7.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
8. 8.What is the distance between the points (0, 1) and (16, 13)? (a) 400 (b) 21 (c) 28 (d) 20
9. 9.In a class of 16 children, 10 like maths, 9 like science and 4 like both. How many like only maths? (a) 7 (b) 6 (c) 10 (d) 5
10. 10.How many factors does 37 have? (a) 3 (b) 1 (c) 2 (d) 4
11. 11.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
12. 12.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 34 (c) 24 (d) 33
13. 13.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
14. 14.In a class of 36 children, 12 like cricket, 20 like football and 2 like both. How many like at least one of the two? (a) 28 (b) 36 (c) 30 (d) 32
15. 15.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 81 (c) 45 (d) 72
16. 16.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
17. 17.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 22 (c) 15 (d) 21
18. 18.In a class of 20 children, 6 like cricket, 9 like football and 2 like both. How many like neither? (a) 7 (b) 2 (c) 5 (d) 9
19. 19.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
20. 20.What is the mode of 18, 17, 2, 2, 18, 18 and 14? (a) 2 (b) 17 (c) 14 (d) 18
21. 21.The mean of 8 numbers is 19. When the number 28 is added to them, what is the new mean? (a) 20 (b) 21 (c) 19 (d) 22
22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 21 (b) 9 (c) 19 (d) 20
23. 23.Two angles of a triangle are 50° and 80°. What is the third angle? (a) 130° (b) 50° (c) 230° (d) 100°
24. 24.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6
25. 25.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 60 (c) 20 (d) 180
26. 26.In a class of 47 children, 24 like tea, 29 like coffee and 12 like both. How many like only tea? (a) 18 (b) 12 (c) 17 (d) 24
27. 27.A drawer has lots of green, black, red and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 4 (c) 5 (d) 8
28. 28.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/18 (c) 1/11 (d) 1/12
29. 29.In a class of 31 children, 13 like tea, 24 like coffee and 10 like both. How many like at least one of the two? (a) 31 (b) 37 (c) 17 (d) 27
30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 7 (b) 19 (c) 17 (d) 18
31. 31.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 21 (b) 29 (c) 22 (d) 28
32. 32.What is the sum of all the whole numbers from 1 to 18? (a) 162 (b) 171 (c) 342 (d) 153
33. 33.Which term of the AP 8, 10, 12, 14, … is 54? (a) 25th (b) 23rd (c) 27th (d) 24th
34. 34.In a class of 41 children, 27 like mangoes, 13 like bananas and 7 like both. How many like only mangoes? (a) 20 (b) 6 (c) 28 (d) 27
35. 35.A cuboid is 9 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 15 cu cm (b) 72 cu cm (c) 124 cu cm (d) 18 cu cm
36. 36.In a class of 44 children, 27 like mangoes, 16 like bananas and 8 like both. How many like only mangoes? (a) 8 (b) 27 (c) 19 (d) 28
37. 37.The mean of 4 numbers is 13. When the number 18 is added to them, what is the new mean? (a) 14 (b) 13 (c) 16 (d) 15
38. 38.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 8 times (c) 4 times (d) 5 times
39. 39.What is the mode of 9, 9, 6, 6, 14, 6 and 4? (a) 9 (b) 14 (c) 6 (d) 4
40. 40.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm

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